Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 89.6% → 96.8%

Time: 9.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (t - z)) / (y - z)
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. associate-/l/ 96.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

3. Simplified 96.9%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

4. Final simplification 96.9%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]

Alternative 2: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t z) y))))
   (if (<= t -1.35e-260)
     t_1
     (if (<= t 6.5e-271)
       (/ (/ x z) z)
       (if (<= t 2.3e-83)
         t_1
         (if (<= t 4.6e+185) (/ x (* t (- y z))) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) * y);
	double tmp;
	if (t <= -1.35e-260) {
		tmp = t_1;
	} else if (t <= 6.5e-271) {
		tmp = (x / z) / z;
	} else if (t <= 2.3e-83) {
		tmp = t_1;
	} else if (t <= 4.6e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - z) * y)
    if (t <= (-1.35d-260)) then
        tmp = t_1
    else if (t <= 6.5d-271) then
        tmp = (x / z) / z
    else if (t <= 2.3d-83) then
        tmp = t_1
    else if (t <= 4.6d+185) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) * y);
	double tmp;
	if (t <= -1.35e-260) {
		tmp = t_1;
	} else if (t <= 6.5e-271) {
		tmp = (x / z) / z;
	} else if (t <= 2.3e-83) {
		tmp = t_1;
	} else if (t <= 4.6e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((t - z) * y)
	tmp = 0
	if t <= -1.35e-260:
		tmp = t_1
	elif t <= 6.5e-271:
		tmp = (x / z) / z
	elif t <= 2.3e-83:
		tmp = t_1
	elif t <= 4.6e+185:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) * y))
	tmp = 0.0
	if (t <= -1.35e-260)
		tmp = t_1;
	elseif (t <= 6.5e-271)
		tmp = Float64(Float64(x / z) / z);
	elseif (t <= 2.3e-83)
		tmp = t_1;
	elseif (t <= 4.6e+185)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) * y);
	tmp = 0.0;
	if (t <= -1.35e-260)
		tmp = t_1;
	elseif (t <= 6.5e-271)
		tmp = (x / z) / z;
	elseif (t <= 2.3e-83)
		tmp = t_1;
	elseif (t <= 4.6e+185)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-260], t$95$1, If[LessEqual[t, 6.5e-271], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 2.3e-83], t$95$1, If[LessEqual[t, 4.6e+185], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35000000000000003e-260 or 6.5000000000000005e-271 < t < 2.2999999999999999e-83

   1. Initial program 89.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 61.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   4. Simplified 61.8%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -1.35000000000000003e-260 < t < 6.5000000000000005e-271

   1. Initial program 84.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 58.4%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 58.4%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 67.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 67.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if 2.2999999999999999e-83 < t < 4.6000000000000003e185

   1. Initial program 92.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 85.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 4.6000000000000003e185 < t

   1. Initial program 75.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 98.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   4. Taylor expanded in t around inf 98.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.4e+41)
     t_1
     (if (<= z -4.2e-171)
       (/ x (* t (- y z)))
       (if (<= z 2e+69) (/ x (* (- t z) y)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.4e+41) {
		tmp = t_1;
	} else if (z <= -4.2e-171) {
		tmp = x / (t * (y - z));
	} else if (z <= 2e+69) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-5.4d+41)) then
        tmp = t_1
    else if (z <= (-4.2d-171)) then
        tmp = x / (t * (y - z))
    else if (z <= 2d+69) then
        tmp = x / ((t - z) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.4e+41) {
		tmp = t_1;
	} else if (z <= -4.2e-171) {
		tmp = x / (t * (y - z));
	} else if (z <= 2e+69) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -5.4e+41:
		tmp = t_1
	elif z <= -4.2e-171:
		tmp = x / (t * (y - z))
	elif z <= 2e+69:
		tmp = x / ((t - z) * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.4e+41)
		tmp = t_1;
	elseif (z <= -4.2e-171)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 2e+69)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -5.4e+41)
		tmp = t_1;
	elseif (z <= -4.2e-171)
		tmp = x / (t * (y - z));
	elseif (z <= 2e+69)
		tmp = x / ((t - z) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.4e+41], t$95$1, If[LessEqual[z, -4.2e-171], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+69], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999999e41 or 2.0000000000000001e69 < z

   1. Initial program 76.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 71.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.6%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 81.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 81.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -5.39999999999999999e41 < z < -4.2e-171

   1. Initial program 91.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 58.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if -4.2e-171 < z < 2.0000000000000001e69

   1. Initial program 96.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 74.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 74.6%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   4. Simplified 74.6%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 4: 80.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-135)
   (/ x (* (- t z) y))
   (if (<= t 1.25e-23)
     (/ (- x) (* z (- y z)))
     (if (<= t 4.8e+185) (/ x (* t (- y z))) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-135) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.25e-23) {
		tmp = -x / (z * (y - z));
	} else if (t <= 4.8e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.7d-135)) then
        tmp = x / ((t - z) * y)
    else if (t <= 1.25d-23) then
        tmp = -x / (z * (y - z))
    else if (t <= 4.8d+185) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-135) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.25e-23) {
		tmp = -x / (z * (y - z));
	} else if (t <= 4.8e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-135:
		tmp = x / ((t - z) * y)
	elif t <= 1.25e-23:
		tmp = -x / (z * (y - z))
	elif t <= 4.8e+185:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-135)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 1.25e-23)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (t <= 4.8e+185)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e-135)
		tmp = x / ((t - z) * y);
	elseif (t <= 1.25e-23)
		tmp = -x / (z * (y - z));
	elseif (t <= 4.8e+185)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e-135], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-23], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+185], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.69999999999999995e-135

   1. Initial program 91.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   4. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -1.69999999999999995e-135 < t < 1.2500000000000001e-23

   1. Initial program 85.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 76.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 76.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 76.9%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 76.9%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

   4. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

   if 1.2500000000000001e-23 < t < 4.79999999999999978e185

   1. Initial program 94.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 86.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 4.79999999999999978e185 < t

   1. Initial program 75.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 98.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   4. Taylor expanded in t around inf 98.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.25e-132)
   (/ x (* (- t z) y))
   (if (<= t 3.3e-26)
     (/ (/ (- x) z) (- y z))
     (if (<= t 5.5e+185) (/ x (* t (- y z))) (/ (/ x t) (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.25e-132) {
		tmp = x / ((t - z) * y);
	} else if (t <= 3.3e-26) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 5.5e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.25d-132)) then
        tmp = x / ((t - z) * y)
    else if (t <= 3.3d-26) then
        tmp = (-x / z) / (y - z)
    else if (t <= 5.5d+185) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.25e-132) {
		tmp = x / ((t - z) * y);
	} else if (t <= 3.3e-26) {
		tmp = (-x / z) / (y - z);
	} else if (t <= 5.5e+185) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.25e-132:
		tmp = x / ((t - z) * y)
	elif t <= 3.3e-26:
		tmp = (-x / z) / (y - z)
	elif t <= 5.5e+185:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.25e-132)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 3.3e-26)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (t <= 5.5e+185)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.25e-132)
		tmp = x / ((t - z) * y);
	elseif (t <= 3.3e-26)
		tmp = (-x / z) / (y - z);
	elseif (t <= 5.5e+185)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.25e-132], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-26], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+185], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25e-132

   1. Initial program 91.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   4. Simplified 60.5%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]

   if -1.25e-132 < t < 3.2999999999999998e-26

   1. Initial program 85.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 76.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 76.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 76.9%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 76.9%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

      4. associate-/r* 88.4%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]

      5. distribute-frac-neg 88.4%

         \[\leadsto \frac{\color{blue}{-\frac{x}{z}}}{y - z} \]

   4. Simplified 88.4%

      \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{y - z}} \]

   if 3.2999999999999998e-26 < t < 5.4999999999999996e185

   1. Initial program 94.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 86.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 5.4999999999999996e185 < t

   1. Initial program 75.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. associate-/l/ 98.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   4. Taylor expanded in t around inf 98.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 6: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+122} \lor \neg \left(z \leq 1.1 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+122) (not (<= z 1.1e+128)))
   (/ (/ (- x) z) (- t z))
   (/ x (* (- t z) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+122) || !(z <= 1.1e+128)) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.2d+122)) .or. (.not. (z <= 1.1d+128))) then
        tmp = (-x / z) / (t - z)
    else
        tmp = x / ((t - z) * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+122) || !(z <= 1.1e+128)) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+122) or not (z <= 1.1e+128):
		tmp = (-x / z) / (t - z)
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+122) || !(z <= 1.1e+128))
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e+122) || ~((z <= 1.1e+128)))
		tmp = (-x / z) / (t - z);
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+122], N[Not[LessEqual[z, 1.1e+128]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e122 or 1.10000000000000008e128 < z

   1. Initial program 72.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around 0 72.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 72.5%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(t - z\right)}} \]

      2. associate-/r* 91.0%

         \[\leadsto -\color{blue}{\frac{\frac{x}{z}}{t - z}} \]

      3. distribute-neg-frac 91.0%

         \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{t - z}} \]

   4. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{t - z}} \]

   if -2.1999999999999999e122 < z < 1.10000000000000008e128

   1. Initial program 93.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+122} \lor \neg \left(z \leq 1.1 \cdot 10^{+128}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 7: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.42e+54)
     t_1
     (if (<= z 6.8e-17)
       (/ (/ x t) y)
       (if (<= z 1.5e+68) (/ (- x) (* z y)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.42e+54) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 1.5e+68) {
		tmp = -x / (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.42d+54)) then
        tmp = t_1
    else if (z <= 6.8d-17) then
        tmp = (x / t) / y
    else if (z <= 1.5d+68) then
        tmp = -x / (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.42e+54) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 1.5e+68) {
		tmp = -x / (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.42e+54:
		tmp = t_1
	elif z <= 6.8e-17:
		tmp = (x / t) / y
	elif z <= 1.5e+68:
		tmp = -x / (z * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.42e+54)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.5e+68)
		tmp = Float64(Float64(-x) / Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.42e+54)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = (x / t) / y;
	elseif (z <= 1.5e+68)
		tmp = -x / (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.42e+54], t$95$1, If[LessEqual[z, 6.8e-17], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.5e+68], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.41999999999999995e54 or 1.5000000000000001e68 < z

   1. Initial program 77.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.8%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 83.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -1.41999999999999995e54 < z < 6.7999999999999996e-17

   1. Initial program 92.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 54.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
   3. Step-by-step derivation

      1. associate-/r* 59.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

      2. div-inv 59.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]

   4. Applied egg-rr 59.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   5. Step-by-step derivation

      1. associate-*l/ 59.8%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t}}{y}} \]

      2. un-div-inv 59.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   6. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 6.7999999999999996e-17 < z < 1.5000000000000001e68

   1. Initial program 99.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 56.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 56.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 56.8%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 56.8%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

   4. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

   5. Taylor expanded in z around 0 33.6%

      \[\leadsto \frac{-x}{\color{blue}{y \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+54}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 8: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.5e+55)
     t_1
     (if (<= z 6.8e-17)
       (/ (/ x t) y)
       (if (<= z 2.2e+68) (/ (/ (- x) z) y) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 2.2e+68) {
		tmp = (-x / z) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-5.5d+55)) then
        tmp = t_1
    else if (z <= 6.8d-17) then
        tmp = (x / t) / y
    else if (z <= 2.2d+68) then
        tmp = (-x / z) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 2.2e+68) {
		tmp = (-x / z) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -5.5e+55:
		tmp = t_1
	elif z <= 6.8e-17:
		tmp = (x / t) / y
	elif z <= 2.2e+68:
		tmp = (-x / z) / y
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.2e+68)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = (x / t) / y;
	elseif (z <= 2.2e+68)
		tmp = (-x / z) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.5e+55], t$95$1, If[LessEqual[z, 6.8e-17], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.2e+68], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000004e55 or 2.19999999999999987e68 < z

   1. Initial program 77.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.8%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 83.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -5.5000000000000004e55 < z < 6.7999999999999996e-17

   1. Initial program 92.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 54.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
   3. Step-by-step derivation

      1. associate-/r* 59.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

      2. div-inv 59.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]

   4. Applied egg-rr 59.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   5. Step-by-step derivation

      1. associate-*l/ 59.8%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t}}{y}} \]

      2. un-div-inv 59.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   6. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 6.7999999999999996e-17 < z < 2.19999999999999987e68

   1. Initial program 99.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 56.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 56.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 56.8%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 56.8%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

   4. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

   5. Taylor expanded in z around 0 33.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 33.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 33.7%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac 33.7%

         \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{z}} \]

      4. distribute-neg-frac 33.7%

         \[\leadsto \frac{\color{blue}{\frac{-x}{y}}}{z} \]

   7. Simplified 33.7%

      \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{z}} \]

   8. Taylor expanded in x around 0 33.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 33.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. *-commutative 33.6%

         \[\leadsto -\frac{x}{\color{blue}{z \cdot y}} \]

      3. distribute-neg-frac 33.6%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot y}} \]

   10. Simplified 33.6%

       \[\leadsto \color{blue}{\frac{-x}{z \cdot y}} \]

   11. Taylor expanded in x around 0 33.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 33.6%

          \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

       2. associate-/l/ 33.6%

          \[\leadsto -\color{blue}{\frac{\frac{x}{z}}{y}} \]

       3. distribute-neg-frac 33.6%

          \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{y}} \]

   13. Simplified 33.6%

       \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 9: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.5e+55)
     t_1
     (if (<= z 6.8e-17)
       (/ (/ x t) y)
       (if (<= z 1.75e+68) (/ (/ (- x) y) z) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 1.75e+68) {
		tmp = (-x / y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-5.5d+55)) then
        tmp = t_1
    else if (z <= 6.8d-17) then
        tmp = (x / t) / y
    else if (z <= 1.75d+68) then
        tmp = (-x / y) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+55) {
		tmp = t_1;
	} else if (z <= 6.8e-17) {
		tmp = (x / t) / y;
	} else if (z <= 1.75e+68) {
		tmp = (-x / y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -5.5e+55:
		tmp = t_1
	elif z <= 6.8e-17:
		tmp = (x / t) / y
	elif z <= 1.75e+68:
		tmp = (-x / y) / z
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.75e+68)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -5.5e+55)
		tmp = t_1;
	elseif (z <= 6.8e-17)
		tmp = (x / t) / y;
	elseif (z <= 1.75e+68)
		tmp = (-x / y) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.5e+55], t$95$1, If[LessEqual[z, 6.8e-17], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.75e+68], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000004e55 or 1.74999999999999989e68 < z

   1. Initial program 77.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.8%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 83.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 83.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -5.5000000000000004e55 < z < 6.7999999999999996e-17

   1. Initial program 92.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 54.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
   3. Step-by-step derivation

      1. associate-/r* 59.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

      2. div-inv 59.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]

   4. Applied egg-rr 59.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   5. Step-by-step derivation

      1. associate-*l/ 59.8%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t}}{y}} \]

      2. un-div-inv 59.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   6. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 6.7999999999999996e-17 < z < 1.74999999999999989e68

   1. Initial program 99.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 56.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 56.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 56.8%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 56.8%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

   4. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

   5. Taylor expanded in z around 0 33.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 33.6%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 33.7%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac 33.7%

         \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{z}} \]

      4. distribute-neg-frac 33.7%

         \[\leadsto \frac{\color{blue}{\frac{-x}{y}}}{z} \]

   7. Simplified 33.7%

      \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+41} \lor \neg \left(z \leq 2.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e+41) (not (<= z 2.8e+20)))
   (/ (/ x z) z)
   (/ x (* t (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+41) || !(z <= 2.8e+20)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d+41)) .or. (.not. (z <= 2.8d+20))) then
        tmp = (x / z) / z
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+41) || !(z <= 2.8e+20)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+41) or not (z <= 2.8e+20):
		tmp = (x / z) / z
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+41) || !(z <= 2.8e+20))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e+41) || ~((z <= 2.8e+20)))
		tmp = (x / z) / z;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+41], N[Not[LessEqual[z, 2.8e+20]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e41 or 2.8e20 < z

   1. Initial program 78.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 68.4%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 68.4%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 77.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -3.2000000000000001e41 < z < 2.8e20

   1. Initial program 94.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 69.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+41} \lor \neg \left(z \leq 2.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 11: 46.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+108} \lor \neg \left(z \leq 7.4 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+108) (not (<= z 7.4e+46))) (/ x (* z y)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+108) || !(z <= 7.4e+46)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+108)) .or. (.not. (z <= 7.4d+46))) then
        tmp = x / (z * y)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+108) || !(z <= 7.4e+46)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+108) or not (z <= 7.4e+46):
		tmp = x / (z * y)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+108) || !(z <= 7.4e+46))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+108) || ~((z <= 7.4e+46)))
		tmp = x / (z * y);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+108], N[Not[LessEqual[z, 7.4e+46]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000003e108 or 7.3999999999999998e46 < z

   1. Initial program 75.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 71.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{\left(y - z\right) \cdot z}} \]
   3. Step-by-step derivation

      1. associate-*r/ 71.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{\left(y - z\right) \cdot z}} \]

      2. neg-mul-1 71.7%

         \[\leadsto \frac{\color{blue}{-x}}{\left(y - z\right) \cdot z} \]

      3. *-commutative 71.7%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot \left(y - z\right)}} \]

   4. Simplified 71.7%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

   5. Taylor expanded in z around 0 45.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 47.4%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac 47.4%

         \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{z}} \]

      4. distribute-neg-frac 47.4%

         \[\leadsto \frac{\color{blue}{\frac{-x}{y}}}{z} \]

   7. Simplified 47.4%

      \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{z}} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 47.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{y}}{z}\right)\right)} \]

      2. expm1-udef 65.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{y}}{z}\right)} - 1} \]

      3. associate-/l/ 65.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{z \cdot y}}\right)} - 1 \]

      4. add-sqr-sqrt 31.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot y}\right)} - 1 \]

      5. sqrt-unprod 60.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z \cdot y}\right)} - 1 \]

      6. sqr-neg 60.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z \cdot y}\right)} - 1 \]

      7. sqrt-unprod 33.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot y}\right)} - 1 \]

      8. add-sqr-sqrt 65.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{z \cdot y}\right)} - 1 \]

   9. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{z \cdot y}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 44.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{z \cdot y}\right)\right)} \]

       2. expm1-log1p 45.2%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]

   11. Simplified 45.2%

       \[\leadsto \color{blue}{\frac{x}{z \cdot y}} \]

   if -8.0000000000000003e108 < z < 7.3999999999999998e46

   1. Initial program 93.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 48.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+108} \lor \neg \left(z \leq 7.4 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 12: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+32} \lor \neg \left(z \leq 6.6 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+32) (not (<= z 6.6e+14))) (/ x (* z z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+32) || !(z <= 6.6e+14)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.8d+32)) .or. (.not. (z <= 6.6d+14))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+32) || !(z <= 6.6e+14)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+32) or not (z <= 6.6e+14):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+32) || !(z <= 6.6e+14))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e+32) || ~((z <= 6.6e+14)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+32], N[Not[LessEqual[z, 6.6e+14]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999983e32 or 6.6e14 < z

   1. Initial program 79.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 67.6%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -4.79999999999999983e32 < z < 6.6e14

   1. Initial program 94.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 54.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+32} \lor \neg \left(z \leq 6.6 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 13: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+54} \lor \neg \left(z \leq 7.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.42e+54) (not (<= z 7.2e+14))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.42e+54) || !(z <= 7.2e+14)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.42d+54)) .or. (.not. (z <= 7.2d+14))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.42e+54) || !(z <= 7.2e+14)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.42e+54) or not (z <= 7.2e+14):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.42e+54) || !(z <= 7.2e+14))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.42e+54) || ~((z <= 7.2e+14)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.42e+54], N[Not[LessEqual[z, 7.2e+14]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.41999999999999995e54 or 7.2e14 < z

   1. Initial program 80.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 68.5%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 68.5%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -1.41999999999999995e54 < z < 7.2e14

   1. Initial program 92.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 53.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
   3. Step-by-step derivation

      1. associate-/r* 58.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

      2. div-inv 58.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]

   4. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   5. Step-by-step derivation

      1. associate-*l/ 59.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t}}{y}} \]

      2. un-div-inv 59.4%

         \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   6. Applied egg-rr 59.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+54} \lor \neg \left(z \leq 7.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 14: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+55} \lor \neg \left(z \leq 8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.12e+55) (not (<= z 8e+14))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e+55) || !(z <= 8e+14)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.12d+55)) .or. (.not. (z <= 8d+14))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e+55) || !(z <= 8e+14)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.12e+55) or not (z <= 8e+14):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.12e+55) || !(z <= 8e+14))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.12e+55) || ~((z <= 8e+14)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.12e+55], N[Not[LessEqual[z, 8e+14]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000006e55 or 8e14 < z

   1. Initial program 80.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 68.5%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 68.5%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

      2. associate-/r* 77.7%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   4. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

   if -1.12000000000000006e55 < z < 8e14

   1. Initial program 92.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 53.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]
   3. Step-by-step derivation

      1. associate-/r* 58.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

      2. div-inv 58.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]

   4. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   5. Step-by-step derivation

      1. associate-*l/ 59.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t}}{y}} \]

      2. un-div-inv 59.4%

         \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   6. Applied egg-rr 59.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+55} \lor \neg \left(z \leq 8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 39.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (t * y)
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.7%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

2. Taylor expanded in z around 0 42.0%

   \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

3. Final simplification 42.0%

   \[\leadsto \frac{x}{t \cdot y} \]

Developer target: 88.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))